The current $I$,potential difference $V_L$ across the inductor,and potential difference $V_C$ across the capacitor in the circuit as shown in the figure are best represented vectorially as:

$A$ coil has self-inductance $L = 0.04 \ H$ and resistance $R = 12 \ \Omega$. When it is connected to a $220 \ V, 50 \ Hz$ supply,what will be the current flowing through the coil (in $A$)?

In an $L-C-R$ series circuit,if $V$,$V_R$,$V_L$,and $V_C$ are the voltages across the source,resistor,inductor,and capacitor respectively at any instant,choose the correct relation.

To light a $50\,W, 100\,V$ lamp,it is connected in series with a capacitor of capacitance $C = \frac{50}{\pi \sqrt{x}} \mu F$ to a $200\,V, 50\,Hz$ $AC$ source. The value of $x$ is........

An $a.c.$ source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If the frequency of the source is changed to $\frac{\omega}{3}$ (while maintaining the same voltage),the current in the circuit is found to be halved. The ratio of reactance to resistance at the original frequency $\omega$ is:

$A$ current of $4 \, A$ flows in a coil when connected to a $12 \, V$ d.c. source. If the same coil is connected to a $12 \, V, (25/\pi) \, Hz$ a.c. source, a current of $2.4 \, A$ flows in the circuit. The inductance of the coil is: (in $ \, mH$)